Water Depth Given Maximum Horizontal Particle Excursion At Node Calculator

Formula Used:

\[ d = \frac{[g]}{(2 \cdot \pi \cdot \frac{X}{H_{wave}} \cdot T_n)^2} \]

Maximum Horizontal Particle Excursion (X):

Wave Height (H_wave):

Natural Free Oscillating Period of a Basin (T_n):

Water Depth at Harbor (d):

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1. What is Water Depth Given Maximum Horizontal Particle Excursion At Node?

Water Depth at Harbor is the vertical distance from the water surface to the seabed or bottom of the harbor. This calculation helps determine the appropriate depth required for safe navigation and harbor operations based on wave characteristics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d = \frac{[g]}{(2 \cdot \pi \cdot \frac{X}{H_{wave}} \cdot T_n)^2} \]

Where:

\( d \) — Water Depth at Harbor (m)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( \pi \) — Archimedes' constant (3.14159)
\( X \) — Maximum Horizontal Particle Excursion (m)
\( H_{wave} \) — Wave Height (m)
\( T_n \) — Natural Free Oscillating Period of a Basin (s)

Explanation: This formula calculates water depth based on wave characteristics and particle motion, considering gravitational effects and basin oscillation periods.

3. Importance of Water Depth Calculation

Details: Accurate water depth calculation is crucial for harbor design, navigation safety, sediment transport studies, and coastal engineering projects. It ensures vessels can safely enter and exit harbors without grounding.

4. Using the Calculator

Tips: Enter maximum horizontal particle excursion in meters, wave height in meters, and natural free oscillating period in seconds. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is maximum horizontal particle excursion?
A: Maximum Horizontal Particle Excursion refers to the maximum distance that a particle can travel horizontally from its initial position under the influence of a wave or current.

Q2: How is wave height defined?
A: Wave Height is formed when two equal waves are going in opposite direction and create the usual up/down motion of the water surface, but the waves don't progress.

Q3: What is natural free oscillating period of a basin?
A: Natural Free Oscillating Period of a Basin referred to as the natural period or resonant period, is the time it takes for a wave to travel from one end of the basin to the other and back again.

Q4: Why is gravitational acceleration included?
A: Gravitational acceleration affects wave motion and particle excursion, making it an essential factor in water depth calculations.

Q5: What are typical values for these parameters?
A: Values vary significantly based on location and conditions. Maximum horizontal particle excursion can range from centimeters to meters, wave heights from decimeters to several meters, and oscillation periods from seconds to minutes.